Calculus: Early Transcendentals 8th Edition

Published by Cengage Learning
ISBN 10: 1285741552
ISBN 13: 978-1-28574-155-0

Chapter 7 - Review - True-False Quiz - Page 537: 7



Work Step by Step

Consider $ \int^{\infty}_{-\infty}2xdx$ Solve the integral. $ \int^{\infty}_{-\infty}2xdx=[x^{2}]_{-\infty}^{\infty}$ $=\infty-\infty$ =Indeterminate Now, $\lim\limits_{t \to \infty}\int^{t}_{-t}2xdx=\lim\limits_{t \to \infty}[x^{2}]_{-\infty}^{\infty}$ $=\lim\limits_{t \to \infty}0$ $=0$ Therefore, $ \int^{\infty}_{-\infty}2xdx\ne \lim\limits_{t \to \infty}\int^{t}_{-t}2xdx$ Hence, the given statement is false.
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